Third comes the triad, a male number; this also has been ordained to be called odd by the arithmeticians. After all these comes the tetrad, [Sidenote: p. 133.] a female number, and this same is also called even, because it is female. Therefore all the numbers taken from the genus are four--but the boundless genus is number--wherefrom is constructed their perfect number, the decad. For 1, 2, 3, 4 become 10, as has before been shown, if the name which is proper to each of the numbers be substantially kept. This is the sacred Tetractys according to Pythagoras which contains within itself the roots of eternal nature, that is, all the other numbers. For the 11, 12 and the rest take the principle of birth from the 10. Of this decad, the perfect number, the four parts are called: number, monad, square and cube. The conjunctions and minglings of which are for the birth of increase, they completing naturally the fruitful number. For when this square is multiplied into itself, it becomes a square squared; but when a square into a cube, it becomes a square cubed; but when a cube into a cube, it becomes a cube cubed. So that all the numbers are seven, in order that the birth of the existing numbers [Sidenote: p. 134.] may come from a hebdomad, which is number, monad, square, cube, square of a square, cube of a square, cube of a cube. Of this hebdomad Simon and Valentinus, having altered the names, recount prodigies, hastening to base upon it their own systems.[209] For Simon calls (it) thus: Mind, Thought, Name, Voice, Reasoning, Desire and He who has Stood, Stands and will Stand: and Valentinus: Mind, Truth, Word, Life, Man, Church and the Father who is counted with them. According to these (ideas) of those trained in the arithmetic philosophy, which they admired as something unknowable by the crowd, and in pursuance of them, they constructed the heresies excogitated by them.